Mathematical Modelling of Vortex Generation Process in the Flowing Part of the Vortex Flowmeter and Selection of an Optimal Turbulence Model

The article is devoted to mathematical modelling of processes, occurring in the flowing part of the vortex flowmeter, by the finite element method. The urgency of the current study is due to the lack of research in this area.
The analysis of research literature devoted to the study of non-stationary vortex shedding processes and other hydrogasdynamics effects occurring in the flowing part of the vortex flowmeter and similar devices has been performed. A brief description of the vortex generation process behind the bluff body placed in a circular cross-section pipe as well as the basic criteria for functional products are presented.
Various mathematical models for describing turbulent flows in pipes with an object or obstruction were investigated. The available software packages suitable for modelling unsteady turbulent flows were analyzed.
The ANSYS software package, in particular CFX module for fluid and gas, as well as various approaches to mathematical modelling were used to simulate the flowing part of the vortex flowmeter. The article provides a brief description of the basic computational domain settings, mesh formation and initial and boundary conditions setting. To verify the numerical calculations, physical experiments on fluid and gas test benches were performed. For this purpose the samples corresponding to the numerical model have been manufactured and tested.
The research findings led us to conclude that in terms of accuracy and calculation time the optimal approach to numerical simulation of vortex generation processes (Karman vortex street) in the vortex flowmeter is the use of the Reynolds-averaged Navier - Stokes equations (or RANS equations) closed by means of a two - equation model of turbulence, known as the $k-{varepsilon}$ model, which is confirmed by comparison with the experimental data.

Keywords

mathematical modelling; turbulence model; flowing part; vortex flowmeter; bluff body.

References

1. Kremlevskiy P.P. Raskhodomery i schetchiki kolichestva [Flowmeters and Counters]. Leningrad, Mashinostroenie, 1989. 701 p.
2. Baker R.C. Flow Measurement Handbook: Industrial Designs, Operating Principles, Performance, and Applications. N.Y., Cambridge University Press, 2000. 524 p. DOI: 10.1017/CBO9780511471100
3. Kremlevskiy P.P. Rashodomery i schetchiki kolichestva veshhestv. Kn. 1[Flowmeters and Counters of Substances Amount. Vol. 1]. St. Petersburg, Politehnica, 2002. 409 p.
4. Kartashev A.L., Krivonogov A.A. [Research of Spatial Hydrodynamic Effects in the Meterbody of the Vortex Flowmeter]. Bulletin of the South Ural State University. Series: Mechanical Engineering Industry, 2015, vol. 15, no. 4, pp. 5-13. (in Russian) DOI: 10.14529/engin150401
5. Faber T.E. Gidroajerodinamika [Fluid Dynamics for Physicists]. Moscow, Postmarcet, 2001. 560 p.
6. Kartashev A.L., Krivonogov A.A. Spatial Hydrodynamic Effects Investigation in the Vortex Flowmeter and Estimation of Numerical Simulation Capability. Nauka JuUrGU. Sekcija tehnicheskih nauk. Materialy 66-j nauchnoj konferencii. [SUSU Science. Section of Technical Sciences. Proceedings of 66th Scientific Conference], 2014, pp. 33-40. (in Russian) Available at: http://dspace.susu.ru/xmlui/bitstream/handle/0001.74/4287/3.pdf
7. Bogdanov V.D., Konyukhov A.V., Krivonogov A.A., Safonov E.V., Dorohov V.A. [Using of Numerical Simulation Methods in the Development of Vortex Flow Meters]. Sensor and Systems, 2012, no. 8 (159), pp. 40-43. (in Russian)
8. Snegiryov A.Yu. Vysokoproizvoditel'nye vychisleniya v tekhnicheskoy fizike. Chislennoe modelirovanie turbulentnykh techeniy [High-Performance Computing in Technical Physics. Numerical Simulation of Turbulent Flows]. St. Petersburg, Polytechnic University, 2009. 143 p. (in Russian)
9. Bailly C., Comete-Bellot G. Turbulence. Springer International Publishing, 2015. 360 p. DOI: 10.1007/978-3-319-16160-0
10. Spalart P.R. Strategies for Turbulence Modelling and Simulations. International Journal of Heat and Fluid Flow, 2000, vol. 21, pp. 252-263. DOI: 10.1016/S0142-727X(00)00007-2
11. Wilcox D.C. Turbulence Modelling for CFD. La Canada, DCW Industries, 1998. 460 p.
12. Spalart P.R., Allmaras S.R. A One-Equation Turbulence Model for Aerodynamic Flows. Technical Report AIAA-92-0439. 30th Aerospace Scinces Meeting and Exibit, 1992. 22 p. DOI: 10.2514/6.1992-439
13. Launder B.E., Spalding D.B. Lectures in Mathematical Models of Turbulence. London, Academic Press, 1972. 169 p.
14. Lapin Ju.V., Strelec M.H. Vnutrennie techenija gazovyh smesej [The Internal Flow of Gas Mixtures]. Moscow, Nauka, 1989. 368 p.
15. Pope, S.B. Turbulent Flows. Cambridge: Cambridge Univ. Press, 2000. 771 p. DOI: 10.1017/CBO9780511840531
16. Orszag S.A., Yakhot V., Flannery W.S., Boysan F., Choudhury D., Maruzewski J., Patel B. Renormalization Group Modelling and Turbulence Simulations. International Conference on Near-Wall Turbulent Flows, Tempe, Arizona, 1993, pp. 1031-1046.
17. Menter F.R. Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA Journal, 1994, vol. 32, no. 8, pp. 1598-1605. DOI: 10.2514/3.12149
18. Menter F.R. Eddy Viscosity Transport Equations and their Relation to the $k-varepsilon$ Model. ASME Journal of Fluids Engineering, 1997, vol. 119, no. 4, pp. 876-884. DOI: 10.1115/1.2819511
19. Menter F.R., Kuntz M., Langtry R. Ten Years of Industrial Experience with the SST Turbulence Model, Turbulence, Heat and Mass Transfer 4, Begell House, 2003, pp. 625-632.
20. Menter F.R. Review of the Shear-Stress Transport Turbulence Model Experience from an Industrial Perspective. International Journal of Computational Fluid Dynamics, 2009, vol. 23, no. 4, pp. 305-316. DOI: 10.1080/10618560902773387
21. Shih T.-H., Liou W.W., Shabbir A., Yang Z., Zhu J. A New $k-varepsilon$ Eddy-Viscosity Model for High Reynolds Number Turbulent Flows - Model Development and Validation. Computers and Fluids, 1995, vol. 24, no. 3, pp. 227-238. DOI: 10.1016/0045-7930(94)00032-T
22. Behnia M., Parneix S., Shabany Y., Durbin P.A. Numerical Study of Turbulent Heat Transfer in Confined and Unconfined Impinging Jets. International Journal of Heat and Fluid Flow, 1999, vol. 20, no. 1, pp. 1-9. DOI: 10.1016/S0142-727X(98)10040-1